(2x-1)(x-2)=5

Solution for (2x-1)(x-2)=5 equation:

Simplifying
(2x + -1)(x + -2) = 5

Reorder the terms:
(-1 + 2x)(x + -2) = 5

Reorder the terms:
(-1 + 2x)(-2 + x) = 5

Multiply (-1 + 2x) * (-2 + x)
(-1(-2 + x) + 2x * (-2 + x)) = 5
((-2 * -1 + x * -1) + 2x * (-2 + x)) = 5
((2 + -1x) + 2x * (-2 + x)) = 5
(2 + -1x + (-2 * 2x + x * 2x)) = 5
(2 + -1x + (-4x + 2x2)) = 5

Combine like terms: -1x + -4x = -5x
(2 + -5x + 2x2) = 5

Solving
2 + -5x + 2x2 = 5

Solving for variable 'x'.

Reorder the terms:
2 + -5 + -5x + 2x2 = 5 + -5

Combine like terms: 2 + -5 = -3
-3 + -5x + 2x2 = 5 + -5

Combine like terms: 5 + -5 = 0
-3 + -5x + 2x2 = 0

Factor a trinomial.
(-1 + -2x)(3 + -1x) = 0

Subproblem 1
Set the factor '(-1 + -2x)' equal to zero and attempt to solve:

Simplifying
-1 + -2x = 0

Solving
-1 + -2x = 0

Move all terms containing x to the left, all other terms to the right.

Add '1' to each side of the equation.
-1 + 1 + -2x = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -2x = 0 + 1
-2x = 0 + 1

Combine like terms: 0 + 1 = 1
-2x = 1

Divide each side by '-2'.
x = -0.5

Simplifying
x = -0.5
Subproblem 2
Set the factor '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-3' to each side of the equation.
3 + -3 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Solution
x = {-0.5, 3}